After reviewing data from a sample, an inference can be made about the population. For example,

Find a data set on the internet. Some suggested search terms: Free Data Sets, Medical Data Sets, Education Data Sets.

Based on the trends and the history of your data set, make a claim. What kind of test (left, right, two tailed) would you have to complete?

Show work

The National Assessment of Educational Progress (NAEP) includes a mathematics test for eighth‑grade students. Scores on the test range from 0 to 500 . Demonstrating the ability to use the mean to solve a problem is an example of the skills and knowledge associated with performance at the Basic level. An example of the knowledge and skills associated with the Proficient level is being able to read and interpret a stem‑and‑leaf plot. In 2015, 136,900 eighth‑graders were in the NAEP sample for the mathematics test. The mean mathematics score was ?¯=282 . We want to estimate the mean score ? in the population of all eighth‑graders. Consider the NAEP sample as an SRS from a Normal population with standard deviation ?=110 . (a) If we take many samples, the sample mean ?¯ varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score ? in the population. What is the standard deviation of this sampling distribution? (Enter your answer rounded to four decimal places.)

(c) What is the 95% confidence interval for the population mean score ? based on this one sample? (Enter your answer rounded to one decimal place.)

Lower value =

Higher value=

Develop an APA formatted paper that defines and presents an analysis of the following concepts in a business application. This means that you must provide examples of how each of these concepts can be used by upper-level management to make strategic decisions, and provide details on how statistical concepts used in the decision-making process can be summarized and presented to a board of directors (for example):

• Types of statistics used for business
• How Computer Software Applications can be used to process and analyze data
• How data can be displayed and explored in an effort to make better strategic business decisions
• How Probability is used in sales, marketing, manufacturing, etc.
• How to test hypotheses and compare results for the purpose of forecasting and making better strategic business decisions.

Suppose three players go on multiple rounds of kart race. In each round, every player has a winning probability of 1/3, independent of other rounds. Let N denote the number of rounds until player 1 has two consecutive wins.

a) Find P(N <= 10)

b) Find P(N = 10)

5.         Wellington Fabrics of New Zealand produces bolts of woolen cloth for export. Each bolt contains 30 yards of fabric. Industry standards call for the average number of defects per fabric bolt to not exceed five. An inspector randomly selected a bolt of cloth, examined the first 3 yards and found 3 defects therein. The company assumes that the defect rate follows the Poisson distribution.

a.          Given the above information, if the company is meeting the industry standards, what is the average number of defects expected in a 3-yard segment of a cloth bolt?

b.         Calculate the probability of finding 3 or more defects in a 3-yard segment of cloth given the above information.

c.          Given your answer to part b., does it appear that the company is meeting the industry standard for quality? Explain briefly.

d.         To verify the findings the inspector examines 15 yards of another bolt of cloth and discovers five defects.

i.          Calculate the average number of defects expected in a 15-yard segment of cloth;

ii.         Calculate the probability of finding five or more defects in the 15-yard cloth segment.

e.          The normal distribution can be used to approximate the Poisson distribution. To calculate a z-score you need the mean and standard deviation. Remember that the mean and variance of a Poisson random variable are equal.

i.          Calculate the mean and standard deviation for the number of defects in a 15-yard segment of cloth.

ii.         Use this mean and standard deviation to calculate the probability of finding five or more defects in a 15-yard segment of cloth using the normal approximation. [Remember to use the continuity correction!]

iii.        How accurate is this approximation?

1. What trends do you notice in your data set?

2.Based on the trends and the history of your data set, make a claim. What kind of test (left, right, two tailed) would you have to complete?

3.Explain the steps needed to complete the Hypothesis Test. What is needed?

Suppose a simple random sample of size nequals49 is obtained from a population with mu equals 71 and sigma equals 7. ​(a) Describe the sampling distribution of x overbar. ​(b) What is Upper P left parenthesis x overbar greater than 72.5 right parenthesis​? ​(c) What is Upper P left parenthesis x overbar less than or equals 68.9 right parenthesis​? ​(d) What is Upper P left parenthesis 69.65 less than x overbar less than 72.65 right parenthesis​?

Use the given data to complete parts​ (a) and​ (b) below.

x y 2.1 4 3.8 1.4 3 3.6 4.8 4.9 ​(a) Draw a scatter diagram of the data.

Choose the correct answer below.

A. 0 2 4 6 0 2 4 6 x y A scatter diagram has a horizontal x-axis labeled from 0 to 6 in increments of 1 and a vertical y-axis labeled from 0 to 6 in increments of 1. The following 4 approximate points are plotted, listed here from left to right: (1.4, 3.8); (3.6, 3); (4, 2.2); (5, 4.8). From left to right, the points have no visibly apparent upward or downward trend.

B. 0 2 4 6 0 2 4 6 x y A scatter diagram has a horizontal x-axis labeled from 0 to 6 in increments of 1 and a vertical y-axis labeled from 0 to 6 in increments of 1. The following 4 approximate points are plotted, listed here from left to right: (2.2, 4); (3, 3.6); (3.8, 1.4); (4.8, 5). From left to right, the points have no visibly apparent upward or downward trend.

C. 0 2 4 6 0 2 4 6 x y A scatter diagram has a horizontal x-axis labeled from 0 to 6 in increments of 1 and a vertical y-axis labeled from 0 to 6 in increments of 1. The following 4 approximate points are plotted, listed here from left to right: (2.2, 5); (3, 1.4); (3.8, 3.6); (4.8, 4). From left to right, the points have no visibly apparent upward or downward trend.

D. 0 2 4 6 0 2 4 6 x y A scatter diagram has a horizontal x-axis labeled from 0 to 6 in increments of 1 and a vertical y-axis labeled from 0 to 6 in increments of 1. The following 4 approximate points are plotted, listed here from left to right: (1.4, 3); (3.6, 3.8); (4, 4.8); (5, 2.1). From left to right, the points have no visibly apparent upward or downward trend.

Compute the linear correlation coefficient. The linear correlation coefficient for the four pieces of data is nothing. ​(Round to three decimal places as​ needed.)

​(b) Draw a scatter diagram of the data with the additional data point left parenthesis 10.3 comma 9.4 right parenthesis.

Choose the correct answer below.

A. 0 4 8 12 0 4 8 12 x y A scatter diagram has a horizontal x-axis labeled from 0 to 12 in increments of 2 and a vertical y-axis labeled from 0 to 12 in increments of 2. The following 4 approximate points are plotted, listed here from left to right: (2.2, 4); (3, 3.6); (3.8, 1.4); (4.8, 5). One additional point is plotted significantly above and to the right of the rest, approximately at (10.4, 9.4).

B. 0 4 8 12 0 4 8 12 x y A scatter diagram has a horizontal x-axis labeled from 0 to 12 in increments of 2 and a vertical y-axis labeled from 0 to 12 in increments of 2. The following 4 approximate points are plotted, listed here from left to right: (1.4, 3.8); (3.6, 3); (4, 2.2); (5, 4.8). One additional point is plotted significantly above and to the right of the rest, approximately at (9.4, 10.4).

C. 0 4 8 12 0 4 8 12 x y A scatter diagram has a horizontal x-axis labeled from 0 to 12 in increments of 2 and a vertical y-axis labeled from 0 to 12 in increments of 2. The following 4 approximate points are plotted, listed here from left to right: (1.4, 4.8); (3.6, 3); (5, 3.8); (9.4, 2.1). One additional point is plotted significantly above the rest, approximately at (4, 10.3).

D. 0 4 8 12 0 4 8 12 x y A scatter diagram has a horizontal x-axis labeled from 0 to 12 in increments of 2 and a vertical y-axis labeled from 0 to 12 in increments of 2. The following 4 approximate points are plotted, listed here from left to right: (3, 3.6); (3.8, 5); (4.8, 1.4); (10.4, 4). One additional point is plotted significantly above and to the left of the rest, approximately at (2.2, 9.4).

Compute the linear correlation coefficient with the additional data point. The linear correlation coefficient for the five pieces of data is nothing. ​(Round to three decimal places as​ needed.) Comment on the effect the additional data point has on the linear correlation coefficient.

A. The additional data point strengthens the appearance of a linear association between the data points.

B. The additional data point does not affect the linear correlation coefficient.

C. The additional data point weakens the appearance of a linear association between the data points.

Explain why correlations should always be reported with scatter diagrams.

A. The scatter diagram is needed to see if the correlation coefficient is being affected by the presence of outliers.

B. The scatter diagram is needed to determine if the correlation is positive or negative.

C. The scatter diagram can be used to distinguish between association and causation.

Click to select your answer(s).

1. Does Early Language Reduce Tantrums? A recent headline reads “Early Language Skills Reduce Preschool Tantrums, Study Finds,” and the article offers a potential explanation for this: “Verbalizing their frustrations may help little ones cope.” The article refers to a study that recorded the language skill level and the number of tantrums of a sample of preschoolers.
   
   1. Is this an observational study or a randomized experiment?
   2. Assuming the sample is representative of the population of all toddlers, can we conclude that “Early Language Skills Reduce Preschool Tantrums”? Why or why not?
   3. Give a potential confounding variable. Explain how your confounding variable is associated with both the explanatory and the response variables.

Discuss the three measures of central tendency. Give an example for each that applies to a police officers production in writing tickets and discusses how the measure is used. What are the advantages and disadvantages for each of the three measures? How do outliers affect each of these three measures? What are some options for handling outliers?

A machine produces metal rods used in automobile suspension system. A random sample of 16 rods is selected, and the diameter measured. The resulting data in millimeters are shown here: 8.23 8.58 8.42 8.18 8.86 8.25 8.69 8.27 8.19 8.96 8.33 8.34 8.78 8.32 8.68 8.41 Calculate a 90% confidence interval on the diameter mean. With 90% confidence, what is the right-value of the confidence interval on the diameter mean?

Poisson

1. Passengers of the areas lines arrive at random and independently to the documentation section at the airport, the average frequency of arrivals is 1.0 passenger per minute.

to. What is the probability of non-arrivals in a one minute interval?

b. What is the probability that three or fewer passengers arrive at an interval of one minute?

C. What is the probability not arrived in a 30 second interval?

d. What is the probability that three or fewer passengers arrive in an interval of 30 seconds?

2. The average number of spots per yard of fabric follows a Poisson distribution. If λ = 0.2 spot per square yard.

to. Determine the probability of finding 3 spots in 2 square yards.

b. What is the probability of finding more than two spots in 4 square yards?

C. What is the average stain in 10 square yards?

Hypergeometric

1. It is known that of 1000 units of ACME cars of a lot of 8000, they are red. If 400 cars were sent to a wholesaler, what is the probability that you will receive a hundred or less red cars. (Assume X = red auto)

a) P (X <= 100) =? (Hypergeometric)

b) P (X> 50) =?

c) E (x) = expected value red cars

I. Continuous Distribution: Normal

1. Long distance telephone calls have a normal distribution with µ x = 8 minutes and σx = 2 minutes. Taking a unit up.

to. What is the probability that a call will last between 4 minutes and 10 minutes?

b. What is the probability that a call will last less than 9 minutes?

C. What is the value of X so that 12% of the experiment values ​​are greater than it?

d. If samples of size 64 are taken:

i. What proportion or probability of the sample means of the calls will be between 7 minutes and 9 minutes?

ii. What proportion or probability of the sample means of the calls is greater than 5 minutes?

iii. Between that two values ​​from the sample mean are 90% of the data.

Exponential

1. The time to fail in hours of a laser beam in a cytometric machina can be modeled by an exponential distribution with λ = .0005

to. What is the probability that a laser will fail more than 10000 hours?

b. What is the probability that a laser will fail less than 20,000 hours?

C. What is the probability that a laser will fail between 10,000 and 20,000 hours?

A brewery needs to purchase glass bottles that can withstand an internal pressure of at least 150 pounds per square inch (psi). A prospective bottle vendor claims its production process yields bottles with a mean strength of 157 psi and a standard deviation of 3 psi.

a. Assume that the strength of the vendor’s bottles is normally distributed. Calculate the probability that a single bottle chosen randomly from this vendor’s factory would fail to meet the brewer’s standard, assuming the vendor’s claim is true.

b.         The brewer tests a sample of 40 bottles from this vendor and finds the mean strength of the sample to be 155.7. Assuming the vendor’s strength claim to be true, what is the probability of obtaining such a sample with a mean this far or farther below the claimed mean? What does this answer suggest about the veracity of the vendor’s claim?

c.          Which of the following changes would make observing a sample as described in part b. more likely:

            i)          Reducing the claimed mean to 156, holding the standard deviation at 3; or

            ii)         Reducing the standard deviation to 2, holding the mean at 157?

            [Note: You do not have to calculate new probabilities to answer this. But be sure you explain the reasoning behind your answers fully using the appropriate formulas]

A certain flight arrives on time 88 percent of the time. Suppose 145 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that

​(a) exactly 128 flights are on time.

​(b) at least 128 flights are on time.

​(c) fewer than 124 flights are on time.

​(d) between 124 and 125​, inclusive are on time.

​(Round to four decimal places as​ needed.)